https://orcid.org/0009-0005-1760-4585
Figures
Abstract
Purpose
Magnetic resonance current density imaging (MRCDI) can non-invasively validate electric field simulations in volume conductor head models. Weak electric currents are injected using scalp electrodes while measuring the MR phase perturbations caused by the tiny magnetic fields (1–2 nT) induced by the current flow in tissue. MRCDI generally has a low signal-to-noise ratio, making it susceptible to technical imperfections and physiological noise. In this technical note, we tested and optimized simultaneous multi-slice (SMS) EPI for time-efficient and robust brain MRCDI.
Methods
MRCDI data was acquired in a phantom and five human brains using SMS-EPI optimized for measuring current-induced phase perturbations. Multiband factors and interslice gaps were systematically varied and the resulting image quality assessed. In particular, the impact of interslice signal leakage on the measured phase was tested.
Results
Current-free acquisitions showed the expected noise amplification with decreasing interslice distances. However, physiological noise generally dominated the human data, masking potential SMS-related penalties and making the overall noise levels identical to single-slice EPI for interslice gaps of at least 12 mm and multiband factors between 3 and 5. Upon application of electric currents, the phantom data revealed subtle artifacts for multiband factors 5 and 6, even for large gaps. Nevertheless, artifacts were absent in the human brain for multiband factors up to 5, where the performance of SMS-EPI approached that of single-slice measurements for sufficient interslice distances.
Citation: Cunha T, Gregersen F, Hanson LG, Thielscher A (2026) Increased brain coverage and efficiency when measuring current-induced magnetic fields by use of simultaneous multi-slice echo-planar MRI. PLoS One 21(1): e0341731. https://doi.org/10.1371/journal.pone.0341731
Editor: Ozlem Ipek, King's College London, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
Received: July 1, 2025; Accepted: January 12, 2026; Published: January 23, 2026
Copyright: © 2026 Cunha et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: Data of the human subjects cannot be shared publicly because of privacy restrictions. The phantom data is fully available at OSF (https://doi.org/10.17605/OSF.IO/DCWUN).
Funding: This study was supported by the Lundbeck Foundation (https://lundbeckfonden.com/, grant R313-2019-622 to AT, grant R324-2019-1784 to LGH) and the German Research Foundation (https://www.dfg.de/, DFG grants TH 1330/6-1 and TH 1330/7-1, part of Research Unit FOR 5429 “MeMoSLAP”). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
Stimulation targeting and dose control in transcranial brain stimulation can benefit from electric field simulations in personalized volume conductor models of the head [1]. Invasive measurements in patients and non-human primates have demonstrated reasonable fits between the simulated and measured fields on average, but also strong deviations in single cases, suggesting the need for improvements [2–4]. Magnetic resonance current density imaging (MRCDI) is a promising non-invasive technique for validating and optimizing electric field simulations. Injection of weak electric currents using scalp electrodes is combined with MRI to reconstruct current density distributions [5]. These currents induce a magnetic flux density distribution that locally changes the precession frequency of the spins in the sample. Consequently, the phase of the measured signal is modulated by ΔBz,c, the component of the current-induced magnetic field that is parallel to the main field . In brain MRCDI in-vivo, the weak electric currents that can safely and comfortably be injected (1–2 mA) [6–8] induce magnetic fields of only a few nT. Recently, we optimized a double-echo gradient echo EPI sequence with short repetition time for single-slice imaging of the small ΔBz,c-induced phase modulations. We demonstrated that it achieves a good sensitivity while being robust to physiological noise due to its high temporal resolution [9]. However, the relatively long scanning time required to measure ΔBz,c with a sufficient signal-to-noise ratio (SNR) can prevent the acquisition of multiple slices to achieve beneficial [10] whole-brain coverage in practical brain MRCDI experiments.
In this technical note, we optimized and validated simultaneous multi-slice (SMS) imaging for a time-efficient increase of brain coverage in EPI-based MRCDI. Unlike standard in-plane parallel imaging which shortens the acquisition time by reducing the number of phase-encoding (PE) steps for each slice, k-space can be fully sampled in SMS acquisitions to minimize SNR losses and reduce the “g-factor” penalty [11]. However, increasing the number of simultaneously acquired slices (i.e., the multiband – MB – factor) can intensify the mixing of signal between slices, visible as so-called “leakage” artifacts [12,13]. Their severity has been vastly mitigated in SMS-EPI by introducing in-plane shifts between the simultaneously acquired slices (“blipped-CAIPI”) and reconstructing using the Slice-GRAPPA method [14], where each slice is separated by convolving the SMS k-space data with the corresponding GRAPPA-like kernels (estimated from a low-resolution single-slice reference scan). The Split Slice-GRAPPA method further reduces the leakage artifacts by trading off the total error during the kernel fitting procedure against the amount of interslice leakage [15].
While SMS-EPI has become a mainstay of functional and diffusion MRI, it has not yet been validated and optimized for MRCDI [16] that is particularly challenging due to its need for highly accurate MR phase data. Guided by our prior studies [7,10] we chose the settings for SMS-EPI that maximize its sensitivity to ΔBz,c while maintaining image quality. Moreover, we optimized the analyses to account for the effects of inhomogeneity on the ΔBz,c images. We then evaluated the quality of the magnetic fields measured with different MB factors and interslice distances, in both phantom and human brain experiments. Although the results also depend on the coil and sequence characteristics, they give insight into the relevant SMS parameter choices for high-quality ΔBz,c measurements. This study also describes procedures and provides reference values for optimizing and evaluating local measurement protocols.
2. Methods
2.1. Data acquisition
Scanning was performed in a 3T MRI scanner (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany) using a 64-channel head coil and the “Multi-Band EPI C2P” sequence (https://www.cmrr.umn.edu/multiband/) developed by the Center for Magnetic Resonance Research (CMRR, Minneapolis, Minnesota, USA). It implements the blipped-CAIPI approach for a more efficient slice separation, with relative in-plane shifts of 1/3 of the field of view (FOV) along the PE direction automatically imposed for MB factors > 2 and no in-plane acceleration. Additionally, it offers two methods for optimizing the slice-separation kernels: the default Split Slice-GRAPPA (“LeakBlock”) [15] and the Slice-GRAPPA [14]. Unless otherwise stated, the former was used for disentangling the slices.
Two k-space traversals followed each excitation pulse, allowing for a higher bandwidth along the PE direction to reduce geometric distortions caused by B0 inhomogeneities [17], while maintaining a long data acquisition period to increase SNR. All experiments were performed with echo times TE = 25.6, 63.5 ms, repetition time TR = 120 ms, flip-angle 30°, matrix size 64 x 64 and voxel dimensions 3.4 x 3.4 x 3 mm3, in accordance with our prior parameter optimizations [7,10]. Each multiband acquisition was time-matched to that of one single slice.
Acquisitions without electric currents were initially performed to assess the noise level in the ΔBz,c measurements, referred to here as “noise floors” (top row of Fig 1C and 1D). Pilot experiments showed no changes in noise levels when a current source outside the scanner room was connected to the electrodes (or to a simple cable loop) via an RF filter built into the penetration panel. Furthermore, we used low-conductivity cables minimizing RF field distortions that affect SNR and accelerated imaging performance. The cables had a similar diameter and the same material properties as those validated in our previous study [18]. Specifically, they were shown not to couple with the RF field, irrespective of the specific chosen cable length (see Fig 4 in [18]). Thus, the noise floor measurements were often performed with the complete electrical setup in place to facilitate quick transition to the experiments with applied currents. Those were performed using a “loop setup”, where the currents are not injected into the sample but flow through a cable placed around it instead (Fig 1B and 1G). This allows for rigorous validation of the measured ΔBz,c, since the magnetic fields from the cable currents can be calculated from the Biot-Savart integrals [19]. Electric currents with an intensity of 2 mA baseline-to-peak were applied, inverting the polarity at the beginning of each repetition of the EPI sequence (bottom row of Fig 1C and 1D).
Phantom: A) Relative positioning of the slices (s0 to s5) across multiband (MB) factors. B) Slice shifting along z with increasing interslice gap. Note that the position of slice s3 (dashed green line) was kept fixed for all interslice gaps and MB factors. C) Adopted current (I) “injection” schemes: no currents (“noise floor” measurements) and 2 mA baseline-to-peak currents with alternating polarity (“MRCDI” measurements). D) Graphical summary of the experiment: for each interslice gap, a set of multiband factors was tested and compared to single-slice measurements of the corresponding slices. Real ΔBz,c measurements obtained with MB factors 3 and 6 and gaps of 6 and 18 mm are given as examples for each of the two current “injection” schemes. Human: E) Relative positioning of the slices (s0 to s4) across multiband factors. F) Slice shifting along z with increasing interslice gap. Note that slice s2 (dashed green line) was the one kept fixed this time. G) Illustration of how the cable loop was placed around subjects’ heads. The current “injection” schemes depicted in C) were also used in the human experiments, and the adopted strategy was similar to the one portrayed in D).
The relative position of the slices is shown in Fig 1A and 1B. A) Summary of the noise levels in the ΔBz,c measurements, as estimated from the spatial standard deviation of the ΔBz,c images obtained without current injection. Results are shown for SMS acquisitions with different MB factors and interslice gaps, and corresponding single-slice (SS) measurements. The SMS acquisitions are represented by data points connected by lines, while individual data points depict the SS results. Note that the slice pairs (s0,s3), (s1,s4) and (s2,s5) shared the same CAIPI shifts in the SMS acquisitions, and therefore the respective data points exhibit the same marker style. B) Magnitude and ΔBz,c images of the fixed slice (s3) obtained with a MB factor of 6 and different interslice gaps. Subtle artifacts are noticeable in the magnitude images for the smallest gap and are indicated by red arrows.
A) Root Mean Square (RMS) error between the measured (ΔBz,c2mA) and simulated (ΔBz,csim) current-induced magnetic fields. Results are shown for multi-slice measurements with different MB factors and interslice gaps, and the corresponding single-slice (SS) measurements. The relative position of the slices is shown in Fig 1A and 1B. Please note that as the interslice gap increased, the outermost slices got closer to the lead, where the current-induced magnetic fields were stronger, also causing increased RMS errors. B) Example of the simulated and measured current-induced magnetic fields, and respective differences for an acquisition with MB factor 6 and interslice gap of 18 mm. Slices sharing the same CAIPI-shift are shown side by side. The black arrows in s2 and s3 highlight the presence of subtle artifacts, likely due to signal leaking from s5 and s0, respectively.
Lastly, a 3D ultra-short TE PETRA [20] structural scan was acquired in each scanning session to image the conductive rubber cable [18] and then simulate ΔBz,c using the Biot-Savart law. The simulations were then subtracted from the measurements with currents to assess their accuracy.
2.2. ΔBz,c computations
ΔBz,c was computed as the difference in the phase images from consecutive repetitions of the double-echo EPI sequence, divided by the phase sensitivity of the sequence to the current-induced magnetic fields (, with
denoting the proton gyromagnetic ratio) [10]. The ΔBz,c images from each echo time were then combined based on their variance, as estimated from the temporal SNR of the magnitude images at the respective echo times [21]. Regions where the ΔBz,c measurements were not considered trustworthy were masked out as described in Text A of S1 File Supporting Information. The ΔBz,c images were finally corrected for geometric distortions caused by
inhomogeneities using field maps estimated from the phase images at the two echo times, as explained in Text B of S1 File Supporting Information.
2.3. Phantom experiments
Experiments were performed on a spherical FBIRN phantom with a diameter of 17 cm and relaxation times comparable to human brain tissue (T1/T2 530/50 ms).
Initially, the “LeakBlock” and Slice-GRAPPA kernels were tested with a MB factor of 6 and a small interslice gap of 6 mm to provoke leakage artifacts. Measurements with and without electric currents were performed, each including 1000 repetitions of the EPI sequence. Piloting showed that, despite the lower noise levels, the Slice-GRAPPA method resulted in severe leakage artifacts in the ΔBz,c measurements with electric currents (Fig C1 in S1 File Supporting Information). Thus, all experiments described below used the “LeakBlock” kernels for slice separation.
In an experiment without currents, the MB factors and interslice gaps
mm were tested (the gap being the nominal distance from the upper to the lower edge of consecutive slices). The slices associated with different MB factors were organized as depicted in Fig 1A, ensuring that at least three slices were directly comparable across MB factors. When varying the interslice distance, one of the slices was kept fixed, making measurements comparable across the different gaps (slice s3, dashed green line in Fig 1A and 1B). Single-slice measurements, as previously validated in [9], were performed at all positions sampled by the SMS acquisitions, each consisting of 500 repetitions of the EPI sequence. Based on the results from the current-free experiment, a reduced parameter space including the MB factors
and the interslice gaps
mm was tested in a new experiment with electric currents. The exclusion of the interslice distances 9 and 12 mm was based on the noisier results (compared to MB 3) obtained for the other MB factors with gaps smaller than 15 mm. A 6 mm gap was still included as the expected worst-case scenario. The slice placement strategy was identical to the one used in the noise floors experiment, with single-slice measurements performed again at all positions covered by the SMS acquisitions (Fig 1A,1B and 1D). The number of repetitions of the EPI sequence was kept at 500.
2.4. Human experiments
Five healthy volunteers with no MRI contraindications were included in this part of the study after written informed consent. They were recruited between 18.08.2022 and 25.01.2023. The study complied with the Helsinki Declaration on human experimentation and was approved by the Ethics Committee of the Capital Region of Denmark (De Videnskabsetisk Medicinske Komitéer, approval number 2206924).
Given the results from the phantom experiments, MB factor 6 was not further tested in humans. However, all interslice gaps between 6 and 18 mm were again included as additional noise sources contaminating human data might make the relative contributions of the leakage artifacts less relevant. This resulted in the following parameter space for both current-free and current-loop experiments: MB and gap
mm (Fig 1E and 1F). Single slices were imaged at all positions sampled by the SMS acquisitions, each including 500 repetitions of the EPI sequence. For each condition tested, the mean and standard deviation of the selected quality metric were computed across the five subjects.
3. Results
3.1. Phantom experiments
The results of the noise floor measurements are summarized in Fig 2. The noise was quantified as the spatial standard deviation of the current-free images, with SMS acquisitions represented by data points connected by lines, and SS measurements depicted as individual data points (Fig 2A). Slice s3 was kept in a fixed position, thus being suited for evaluating the effects of varying interslice gaps. As expected, the noise levels generally decreased as the gap increased. This was particularly noticeable for MB 6, suggesting that challenging SMS data benefits most from the larger variation in the coil sensitivities along z attained with larger gaps. Examples of magnitude and
noise floor images of slice s3 are shown in Fig 2B for MB 6. Subtle artifacts are seen in the magnitude images for the smallest interslice distance, and the previously mentioned attenuation of the random noise in
with increasing gap is clearly visible.
Since the absolute positions of the remaining slices changed with the interslice distance, the MB factors should be compared for each specific gap (Fig 2A). The biggest differences occurred for the smallest gaps: MB 3 resulted in similar noise levels across all slices, while higher MB factors seem to have suffered from noise “coupling” between specific pairs of slices, which is likely related to the imposed CAIPI shifts. For example, slice s2 showed higher noise levels for MBs 4–6 than for MB 3, and its noise behavior with increasing gaps mirrored that of slice s5. Indeed, slice s5 was absent for MB 3 and otherwise shared the same in-plane CAIPI shift as slice s2, which likely increased the signal leakage between them. A similar behavior was observed for the slice pairs (s1,s4) and (s0,s3) for MBs 5–6 and MB 6, respectively. Increasing the gap to 15 mm resulted in comparable noise levels across MBs 3–5 and brought them substantially closer to those measured for conventional single-slice acquisitions. Higher levels were still observed in some slices for MB 6.
The performance of single-slice and SMS acquisitions upon application of electric currents is summarized in Fig 3A. Shown are the root mean square (RMS) errors between the measured and the simulations based on the Biot-Savart Law. In general, higher MB factors tended to result in slightly larger errors, although this trend was weak. In particular, MB factors 3–4 consistently showed equally good performance, comparable to single-slice acquisitions. MB factor 5 with an 18 mm gap and MB 6 with 15/18 mm gaps showed slightly increased noise levels. For those conditions, subtle artifacts occurred in some slices, potentially caused by signal leaking between slices sharing the same CAIPI shift – the black arrows in Fig 3B indicate examples where leakage between the slice pairs (s2,s5) and (s0, s3) seem to occur. Please note that, due to the chosen cable configuration, the magnetic fields increase along the z direction. Thus, the increase of the absolute RMS errors for the higher slices (most obvious for slice s5) does not indicate a lower measurement quality at those positions, but rather reflects that the chosen error metric scales with the
strength.
3.2. Human experiment
SMS showed generally worse SNR over the time series of magnitude images than single-slice acquisitions. This often resulted in the exclusion of slightly larger brain regions during the first step of the masking procedure described in Text A of S1 File Supporting Information. However, taking single-slice measurements as reference, the number of voxels in the masks stayed clearly above 90% even for MB 5 (on average across subjects; Fig C2 in S1 File Supporting Information). In the current-free experiment, a low number of acquisitions were affected by measurement instabilities of unclear origin. Therefore, noise floor images with RMS values exceeding the average by two standard deviations were considered outliers, resulting in the exclusion of 3 out of 95 single-slice and 2 out of 75 SMS acquisitions.
Fig 4A summarizes the noise floor measurements in humans, quantified as before by the spatial standard deviation of the current-free images. Each data point and vertical error bar represent the average and standard deviation across five subjects. The noise levels stayed below 0.2 nT in all measurements. SMS suffered from larger noise levels than single-slice acquisitions, mostly for the smallest gap (6 mm), while this effect decreased for larger interslice distances. All three tested MB factors performed similarly. In Fig 4B, a representative example of the noise floor images obtained with a MB factor of 5 and a 12 mm gap is given, along with the corresponding single-slice measurements.
The accuracy of the measurements with currents in the cable loop was also assessed through comparison with the Biot-Savart simulations (Fig 5A). The results are quantitatively described by the root mean square (RMS) error between measurements and simulations. The observed errors did not differ substantially between the three MB factors tested and were similar to the single-slice acquisitions. RMS errors below 0.3 nT were obtained for most measurements, with higher errors observed for the top slice (s4) especially for the largest gaps, which placed it in higher brain regions. Fig 5B shows representative results with a MB factor of 5 and a 12 mm gap, along with the corresponding single-slice measurements. There was good agreement between the
measured with the two acquisition types and the simulations, with no severe penalty resulting from the high acceleration factor.
The relative position of the slices is shown in Fig 1E and 1F. A) Summary of the noise levels in the ΔBz,c measurements, as estimated from the spatial standard deviation of the ΔBz,c images obtained without current injection. Results are shown for multi-slice measurements with different MB factors and interslice gaps, and the corresponding single-slice (SS) measurements. Each data point and vertical error bar represent the average and standard deviation across five subjects. B) ΔBz,c noise floor images from an SMS acquisition with a MB factor of 5 and an interslice gap of 12 mm (first row), and corresponding single-slice acquisitions (second row).
The relative position of the slices and loop placement are shown in Fig 1E-1G. A) Root Mean Square (RMS) error between the measured (ΔBz,c2mA) and simulated (ΔBz,csim) current-induced magnetic fields. Results are shown for multi-slice measurements with different multiband (MB) factors and interslice gaps, and the corresponding single-slice (SS) measurements. Each data point and vertical error bar represent the average and standard deviation across subjects. B) Comparison between a multi-slice acquisition with a MB factor of 5 and an interslice gap of 12 mm, and corresponding single-slice acquisitions. Left: simulated and measured magnetic fields. Right: differences between the measured and simulated fields.
4. Discussion
In this study, we optimized and validated SMS-EPI acquisitions of current-induced magnetic fields for human brain MRCDI. Initial phantom tests without current flow confirmed the expected increase of the noise levels with decreasing interslice gaps and increasing MB factors, which both make the separation of signals from different slices more difficult [22,23]. Moreover, closer inspection of the noise floors highlighted the importance of the in-plane CAIPI shifts for reducing interslice leakage. For example, with MB 3, the imposed shifts (in multiples of ) ensured that all slices were shifted in relation to each other. In contrast, with MB 4, the top and bottom slices shared the same shift, making their separation harder and increasing noise floors in both slices. Importantly, however, the relevance of interslice leakage decreased with increasing interslice gaps, and MBs 4 and 5 reached similar noise levels to MB 3 for gaps of 12 mm or more.
In subsequent phantom tests with current flow in a cable loop, SMS revealed error levels (compared to simulations) that remained similar to those of single-slice acquisitions across the tested parameter space.
The current-free human brain measurements also showed noise levels comparable to those of single-slice acquisitions for all tested MB factors with interslice gaps of 12 mm or more. Accordingly, a combination of MB 5 with a 12 mm gap appears as a promising setting for SMS-EPI-based brain MRCDI, providing good brain coverage and maintaining low noise levels.
In the measurements with current flow, increased along the z direction due to the chosen cable configuration both in the phantom and human experiments. As our error metric relies on absolute differences between measurements and simulations, the increasing error levels with increasing interslice gaps observed in the higher slices (strongest for slices s5 and s4 in Fig 3 and 5, respectively) are thus expected. Since good quality noise floors were measured in those slices, we believe that the observed errors do not reflect a lower measurement quality but are mainly caused by inaccuracies in the Biot-Savart simulations due to imprecise cable tracking, in line with our previous observations [19].
The generalization of these findings to other MRCDI setups requires careful consideration. Multiband imaging performance depends on the spatial distribution of the receive coil elements. Moreover, the use of high-conductivity electrode cables may be detrimental to SMS by introducing additional coupling between coils. Here, this problem was avoided by using cables made of low-conductivity silicon rubber [18].
SMS imaging is generally combined with in-plane acceleration to achieve higher acceleration factors [23,24,25] at the cost of reduced SNR and increased “g-factor” penalty. In-plane acceleration is, however, not suitable for EPI-based MRCDI. In fact, reducing the duration of each EPI readout will not substantially reduce the total acquisition time of each measurement, as the echo times (and consequently, repetition time) need to be long enough to allow for sufficient current-induced phase accumulation.
A remaining limitation of our EPI-based MRCDI method (both for SMS and single-slice) is the inefficient spoiling of signal from long T2* tissues, leading to the exclusion of parts of the cerebrospinal fluid (CSF) during the masking procedure. Improving spoiling to obtain usable data from CSF would require increasing the spoiler gradient strengths [6], which was hindered by the lack of access to the source code of the sequence. Furthermore, flow sensitivity would remain.
5. Conclusion
SMS-EPI provided good measurements of the current-induced magnetic fields that were mostly on par with single-slice results, therefore offering an attractive time-efficient way of increasing brain coverage in MRCDI. Within the tested parameter space, only the smallest interslice gap of 6 mm exhibited higher noise floors in humans compared to single-slice acquisitions, while the remaining combinations of MB factors and gaps performed identically.
Our findings suggest flexibility in the choice of parameters based on the desired brain coverage. For example, combining a moderate interslice distance (e.g., 12 mm) with MB factors no larger than 5 will vastly improve brain coverage compared to single-slice EPI, while maintaining a similar quality of the measured magnetic fields. While measurement quality is also influenced by the specific coil, electrodes and sequence implementation used, our study generally confirms the advantages of SMS-EPI for highly sensitive measurements in brain MRCDI.
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